Continuum percolation:
Many phenomena in physics, chemistry, and biology can be modelled by spatial random processes. One such process is continuum percolation, which is used when the phenomenon being modelled is made up of individual events that overlap, for example, the way individual raindrops eventually make the groun...
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| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1996
|
| Edition: | first published |
| Series: | Cambridge tracts in mathematics
119 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | Many phenomena in physics, chemistry, and biology can be modelled by spatial random processes. One such process is continuum percolation, which is used when the phenomenon being modelled is made up of individual events that overlap, for example, the way individual raindrops eventually make the ground evenly wet. This is a systematic rigorous account of continuum percolation. Two models, the Boolean model and the random connection model, are treated in detail, and related continuum models are discussed. All important techniques and methods are explained and applied to obtain results on the existence of phase transitions, equality and continuity of critical densities, compressions, rarefaction, and other aspects of continuum models. This self-contained treatment, assuming only familiarity with measure theory and basic probability theory, will appeal to students and researchers in probability and stochastic geometry |
| Physical Description: | 1 Online-Ressource (x, 238 Seiten) |
| ISBN: | 9780511895357 |
| DOI: | 10.1017/CBO9780511895357 |
Staff View
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| 100 | 1 | |a Meester, Ronaldus W. |d 1963- |0 (DE-588)172254019 |4 aut | |
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| 490 | 1 | |a Cambridge tracts in mathematics |v 119 | |
| 505 | 8 | |a 1. Introduction -- 2. Basic methods -- 3. Occupancy and Poisson Boolean models -- 4. Vacancy in Poisson Boolean models -- 5. Distinguishing features of the Poisson Boolean model -- 6. The Poisson random-connection model -- 7. Models driven by general processes -- 8. Other continuum percolation models | |
| 520 | |a Many phenomena in physics, chemistry, and biology can be modelled by spatial random processes. One such process is continuum percolation, which is used when the phenomenon being modelled is made up of individual events that overlap, for example, the way individual raindrops eventually make the ground evenly wet. This is a systematic rigorous account of continuum percolation. Two models, the Boolean model and the random connection model, are treated in detail, and related continuum models are discussed. All important techniques and methods are explained and applied to obtain results on the existence of phase transitions, equality and continuity of critical densities, compressions, rarefaction, and other aspects of continuum models. This self-contained treatment, assuming only familiarity with measure theory and basic probability theory, will appeal to students and researchers in probability and stochastic geometry | ||
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Record in the Search Index
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| author | Meester, Ronaldus W. 1963- Roy, Rahul |
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| contents | 1. Introduction -- 2. Basic methods -- 3. Occupancy and Poisson Boolean models -- 4. Vacancy in Poisson Boolean models -- 5. Distinguishing features of the Poisson Boolean model -- 6. The Poisson random-connection model -- 7. Models driven by general processes -- 8. Other continuum percolation models |
| ctrlnum | (ZDB-20-CBO)CR9780511895357 (OCoLC)992869473 (DE-599)BVBBV043941848 |
| dewey-full | 530.1/3 |
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| discipline | Physik Mathematik |
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| edition | first published |
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| id | DE-604.BV043941848 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511895357 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350818 |
| oclc_num | 992869473 |
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| physical | 1 Online-Ressource (x, 238 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Meester, Ronaldus W. 1963- (DE-588)172254019 aut Continuum percolation Ronald Meester ; University of Utrecht ; Rahul Roy ; Indian Statistical Institute first published Cambridge Cambridge University Press 1996 1 Online-Ressource (x, 238 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 119 1. Introduction -- 2. Basic methods -- 3. Occupancy and Poisson Boolean models -- 4. Vacancy in Poisson Boolean models -- 5. Distinguishing features of the Poisson Boolean model -- 6. The Poisson random-connection model -- 7. Models driven by general processes -- 8. Other continuum percolation models Many phenomena in physics, chemistry, and biology can be modelled by spatial random processes. One such process is continuum percolation, which is used when the phenomenon being modelled is made up of individual events that overlap, for example, the way individual raindrops eventually make the ground evenly wet. This is a systematic rigorous account of continuum percolation. Two models, the Boolean model and the random connection model, are treated in detail, and related continuum models are discussed. All important techniques and methods are explained and applied to obtain results on the existence of phase transitions, equality and continuity of critical densities, compressions, rarefaction, and other aspects of continuum models. This self-contained treatment, assuming only familiarity with measure theory and basic probability theory, will appeal to students and researchers in probability and stochastic geometry Percolation (Statistical physics) Stochastic processes Perkolation (DE-588)4115530-0 gnd rswk-swf Perkolation (DE-588)4115530-0 s DE-604 Roy, Rahul (DE-588)170929159 aut Erscheint auch als Druck-Ausgabe 978-0-521-47504-4 Erscheint auch als Druck-Ausgabe 978-0-521-06250-3 Cambridge tracts in mathematics 119 (DE-604)BV047362617 119 https://doi.org/10.1017/CBO9780511895357 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Meester, Ronaldus W. 1963- Roy, Rahul Continuum percolation Cambridge tracts in mathematics 1. Introduction -- 2. Basic methods -- 3. Occupancy and Poisson Boolean models -- 4. Vacancy in Poisson Boolean models -- 5. Distinguishing features of the Poisson Boolean model -- 6. The Poisson random-connection model -- 7. Models driven by general processes -- 8. Other continuum percolation models Percolation (Statistical physics) Stochastic processes Perkolation (DE-588)4115530-0 gnd |
| subject_GND | (DE-588)4115530-0 |
| title | Continuum percolation |
| title_auth | Continuum percolation |
| title_exact_search | Continuum percolation |
| title_full | Continuum percolation Ronald Meester ; University of Utrecht ; Rahul Roy ; Indian Statistical Institute |
| title_fullStr | Continuum percolation Ronald Meester ; University of Utrecht ; Rahul Roy ; Indian Statistical Institute |
| title_full_unstemmed | Continuum percolation Ronald Meester ; University of Utrecht ; Rahul Roy ; Indian Statistical Institute |
| title_short | Continuum percolation |
| title_sort | continuum percolation |
| topic | Percolation (Statistical physics) Stochastic processes Perkolation (DE-588)4115530-0 gnd |
| topic_facet | Percolation (Statistical physics) Stochastic processes Perkolation |
| url | https://doi.org/10.1017/CBO9780511895357 |
| volume_link | (DE-604)BV047362617 |
| work_keys_str_mv | AT meesterronaldusw continuumpercolation AT royrahul continuumpercolation |